Structured scanning platform for rapidly capturing design manuscript and deviation correction method

Abstract

The invention relates to the technical field of computer vision and computational photography, in particular to a structured scanning platform for quickly capturing a design manuscript and a deviation rectifying method, which comprises the following modules: a multi-modal sensing module for projecting a phase shift stripe sequence and acquiring a modulation image, solving an absolute phase by using a multi-frequency heterodyne method, and obtaining physical point cloud data of the surface of the design draft based on triangulation; and the discrete geometric modeling module constructs the physical point cloud data into a pure complex grid by using Delauni triangulation, calculates the Euclidean distance of the side length of the grid as a discrete Riemannian metric value, and constructs a discrete Hough star operator. In the invention, through an active optical flow closed-loop feedback mechanism, the Lie derivative flow is driven by phase residual error to iteratively correct the discrete Riemannian metric, and then high-fidelity physical expansion is realized, so that the problems that open-loop geometric projection is mostly adopted in the traditional correction technology, and physical precision verification is lacked, so that the correction precision is poor are solved. And therefore, the problems of scale distortion and texture distortion after the precision drawing is digitalized can be solved.

Description

Technical Field

[0001] This invention relates to the field of image recognition technology, and in particular to a structured scanning platform and correction method for rapid capture of design drafts. Background Technology

[0002] In fields such as aerospace, shipbuilding, and historical archive preservation, there are numerous large-format, precision engineering design drafts drawn on tracing paper or blueprints. Due to long-term curled storage or material aging, these drawings often exhibit non-rigid three-dimensional curling and irregular wrinkles. Existing non-contact scanning correction technologies typically employ vision-based 3D reconstruction and parametric unfolding algorithms, mapping curved surfaces onto a two-dimensional plane.

[0003] However, most traditional correction techniques use open-loop geometric projection, which, due to the lack of physical accuracy verification, results in problems such as scale distortion and texture distortion after the digitization of precise drawings. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a structured scanning platform and correction method for rapid capture of design drafts. It aims to improve the problems of scale distortion and texture distortion caused by the lack of physical accuracy verification in traditional correction techniques, which mostly use open-loop geometric projection.

[0005] In a first aspect, the present invention provides the following technical solution: a structured scanning platform for rapid capture of design drafts, comprising the following modules:

[0006] The multimodal sensing module projects a phase-shifted fringe sequence and acquires modulated images, uses the multi-frequency heterodyne method to solve the absolute phase, and obtains physical point cloud data of the design surface based on triangulation.

[0007] The discrete geometry modeling module uses Deloni triangulation to construct a simple complex mesh from physical point cloud data, calculates the Euclidean distance of the mesh edge length as the discrete Riemann metric, and constructs the discrete Hodge star operator.

[0008] The topology orientation correction module calculates the Gaussian curvature of the grid vertices based on discrete Riemannian metric values ​​and uses the Levi-Civita connection to solve the energy minimization equation to obtain the parallel moving field distributed along the geodesics.

[0009] The conformal parameterized expansion module constructs an initial gradient field based on a parallel moving field, decomposes the initial gradient field using Hodge decomposition and forcibly removes the curl component, reconstructs and corrects the gradient field using the retained components, and solves the Poisson equation to obtain the two-dimensional expanded coordinates.

[0010] The active optical verification module uses two-dimensional unfolded coordinates to establish an inverse mapping relationship, converts the standard grid into an inverse projection image and projects it back onto the physical surface, and calculates the difference norm between the acquired feedback image and the standard phase to generate a phase residual field.

[0011] The closed-loop feedback compensation module calculates the gradient flow of the phase residual field, updates the discrete Riemann metric value based on the gradient flow using the Lie derivative, and returns to the discrete geometric modeling module to perform iterations until the phase residual field satisfies the convergence condition.

[0012] By adopting the above technical solution, the active optical flow closed-loop feedback mechanism uses the phase residual to drive the Lie derivative number flow to iteratively correct the discrete Riemann metric, thereby achieving high-fidelity physical unfolding. This improves the problem that traditional correction techniques mostly use open-loop geometric projection, which, due to the lack of physical accuracy verification, causes scale distortion and texture warping after the digitization of precision drawings.

[0013] Preferably, the multimodal sensing includes:

[0014] Project a sequence of sinusoidal fringes with three different frequencies onto the design draft;

[0015] The acquired modulated image is subjected to phase unwrapping operation to restore the truncated phase to continuous phase;

[0016] Phase ambiguity is eliminated by utilizing the principle of phase difference between different frequencies, thus obtaining a unique absolute phase distribution;

[0017] Stereo matching of left and right images is performed based on epipolar constraints of a binocular camera, and the three-dimensional depth coordinates of each pixel are calculated using the parallax principle.

[0018] Preferably, the discrete geometric modeling includes:

[0019] Traverse every common edge in the simple complex mesh;

[0020] Identify the two adjacent triangular faces shared by the common edge;

[0021] Determine the angles of the vertices opposite the common edge in these two triangular facets;

[0022] Calculate the cotangent of the angle between these two relative vertices;

[0023] Sum the two cotangent values ​​and take the average value. Assign the result to the weight coefficient of the common edge in the diagonal matrix of the discrete Hodge star operator.

[0024] Preferably, the topology orientation correction includes:

[0025] The difference between the sum of the vertex angles of all triangles surrounding a vertex inside the grid and the inscribed angle is used as the angular deficit to determine the discrete Gaussian curvature.

[0026] Construct a least-squares energy equation that includes a smoothing term and an integrity constraint term. The smoothing term is used to constrain the smooth transition of rotation angles between adjacent edges, and the integrity constraint term requires that the sum of rotation angles along a closed path equals the total curvature of the region enclosed by the path.

[0027] The rotation angle of each edge in the grid is obtained by minimizing the energy equation by solving the sparse linear equation system.

[0028] Preferably, the conformal parametric expansion includes:

[0029] Define the discrete forms of the gradient operator and curl operator;

[0030] The initial gradient field is projected onto a first subspace consisting of an irrotational field, a second subspace consisting of a divergence-free field, and a third subspace consisting of a harmonic field.

[0031] Extract the gradient component projection from the first subspace and the harmonic component projection from the third subspace;

[0032] Ignore the projection of the curl component in the second subspace;

[0033] The extracted gradient component projections and harmonic component projections are vector synthesized to generate a corrected gradient field that contains only conformal transformation features.

[0034] Preferably, the conformal parametric expansion further includes:

[0035] Calculate the divergence value of the modified gradient field at each grid vertex;

[0036] Construct a sparse coefficient matrix, which is composed of discrete Laplace-Beltrami operators, and the operators are weighted using the weights of discrete Hodge star operators;

[0037] Use the divergence value as the source term vector;

[0038] Introduce Dirichlet boundary conditions or Neumann boundary conditions to fix the degrees of freedom of the solution;

[0039] The sparse linear equations are solved using the conjugate gradient method to obtain the UV texture coordinates of each vertex on the two-dimensional plane.

[0040] The bicubic interpolation algorithm is used to map pixel grayscale values ​​from the original texture image based on UV texture coordinates.

[0041] Preferably, the active optical verification includes:

[0042] In a two-dimensional unfolded coordinate system, determine the two-dimensional grid patch to which each pixel in the inverse projected image belongs;

[0043] Calculate the centroid coordinates of the pixel within the two-dimensional grid patch;

[0044] The vertex coordinates of the corresponding facet of the three-dimensional simple complex mesh are interpolated using the centroid coordinates to obtain the three-dimensional physical space coordinates of the pixel.

[0045] Using the intrinsic and extrinsic parameter matrices of the projection unit, the three-dimensional physical space coordinates are transformed into pixel row and column coordinates of the projection plane to generate the inverse projection image to be projected.

[0046] Preferably, the active optical verification further includes:

[0047] The measured phase distribution of the physical surface is obtained by phase-shift demodulating the acquired feedback image;

[0048] The corresponding theoretical phase distribution is directly generated based on the generation logic of the inverse projection image;

[0049] Pixel-by-pixel alignment is performed between the measured phase distribution and the theoretical phase distribution;

[0050] Calculate the L2 norm of the difference between the measured phase value and the theoretical phase value at the same pixel location, and use this norm as the phase residual value at that location.

[0051] Preferably, the closed-loop feedback compensation includes:

[0052] Calculate the spatial gradient vector of the phase residual field on the surface of the discrete manifold;

[0053] The spatial gradient vector is defined as the deformation velocity field of the manifold;

[0054] Calculate the Lie derivative of the current discrete Riemannian metric tensor along the deformation velocity field, that is, calculate the infinitesimal deformation rate of the metric tensor under the action of the velocity field.

[0055] The deformation rate is multiplied by the adaptive step size coefficient and then added to the current discrete metric value of the side length to obtain a new metric value containing physical deformation compensation information.

[0056] Secondly, the present invention provides the following technical solution: a method for quickly capturing and correcting deviations in design drafts, comprising the following steps:

[0057] S1. By projecting phase-shifted fringe sequences and acquiring modulated images, the absolute phase is calculated using the multi-frequency heterodyne method, and physical point cloud data of the design surface is obtained based on triangulation.

[0058] S2. Using Deloni triangulation, the physical point cloud data is constructed into a simple complex mesh. The Euclidean distance of the mesh edge length is calculated as the discrete Riemann metric, and the discrete Hodge star operator is constructed.

[0059] S3. Calculate the Gaussian curvature of the grid vertices based on the discrete Riemannian metric, and use the Levi-Civita connection to solve the minimum energy equation to obtain the parallel moving field distributed along the geodesic.

[0060] S4. Construct an initial gradient field based on the parallel moving field, decompose the initial gradient field using Hodge decomposition and forcibly remove the curl component, reconstruct the corrected gradient field using the retained components and solve the Poisson equation to obtain the two-dimensional expanded coordinates.

[0061] S5. Establish an inverse mapping relationship using two-dimensional unfolded coordinates, convert the standard grid into an inverse projection image and project it back onto the physical surface, and calculate the difference norm between the acquired feedback image and the standard phase to generate the phase residual field.

[0062] S6. Calculate the gradient flow of the phase residual field, update the discrete Riemann metric value based on the gradient flow using the Lie derivative, and return to the discrete geometry modeling module to perform iterations until the phase residual field satisfies the convergence condition.

[0063] The present invention has the following beneficial effects:

[0064] 1. In this invention, the phase residual is used to drive the Lie derivative number flow to iteratively correct the discrete Riemann metric, thereby achieving high-fidelity physical unfolding. This improves the problem that traditional correction techniques mostly use open-loop geometric projection, which, due to the lack of physical accuracy verification, causes scale distortion and texture warping after the digitization of precision drawings.

[0065] 2. In this invention, a phase residual field is generated by an active optical verification module and a closed-loop feedback compensation module is used to correct the discrete Riemann metric value based on the Lie derivative, thereby achieving adaptive iterative convergence of the physical entity. This improves the problem that traditional correction techniques mostly adopt open-loop unidirectional processing, which lacks a physical entity verification mechanism, resulting in insufficient geometric accuracy due to the inability to compensate for material nonlinearity errors.

[0066] 3. In this invention, the energy equation is solved by the Levichita connection through the topology direction correction module to obtain the parallel movement field distributed along the geodesic, thereby providing a globally consistent direction constraint for texture unfolding. This improves the problem that traditional manifold unfolding mostly uses local tangent plane splicing, which ignores the influence of intrinsic curvature on vector transmission, resulting in texture direction disorder in areas with drastic curvature changes.

[0067] 4. In this invention, a discrete geometric modeling module is used to construct a simple complex mesh based on the physical point cloud and calculate the discrete Riemann metric value, thereby establishing a discrete manifold model that describes the intrinsic properties of the surface. This improves the problem that traditional scanning processing mostly uses two-dimensional pixel interpolation, which ignores the topological characteristics of the manifold structure and results in low geometric restoration when processing complex and curled surfaces. Attached Figure Description

[0068] Figure 1 This is a module architecture diagram of a structured scanning platform for rapid capture of design drafts proposed in this invention;

[0069] Figure 2 This is a flowchart of a conformal parametric expansion sub-process of a structured scanning platform for rapid capture of design drafts proposed in this invention;

[0070] Figure 3 This is a flowchart of a closed-loop feedback compensation sub-process of a structured scanning platform for rapid capture of design drafts proposed in this invention.

[0071] Figure 4 This is a flowchart of a method for quickly capturing design drafts, as proposed in this invention. Detailed Implementation

[0072] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] Example 1:

[0074] In a first embodiment of the present invention, the present invention provides a structured scanning platform for rapid capture of design drafts, such as... Figures 1-3 As shown, it includes the following modules:

[0075] The multimodal sensing module projects a phase-shifted fringe sequence and acquires modulated images, uses the multi-frequency heterodyne method to solve the absolute phase, and obtains physical point cloud data of the design surface based on triangulation.

[0076] Furthermore, multimodal sensing includes:

[0077] Project a sequence of sinusoidal fringes with three different frequencies onto the design draft;

[0078] The acquired modulated image is subjected to phase unwrapping operation to restore the truncated phase to continuous phase;

[0079] Phase ambiguity is eliminated by utilizing the principle of phase difference between different frequencies, thus obtaining a unique absolute phase distribution;

[0080] Stereo matching of left and right images is performed based on epipolar constraints of a binocular camera, and the three-dimensional depth coordinates of each pixel are calculated using the parallax principle.

[0081] Specifically, the module receives a trigger command from the central controller, and the DLP projection unit projects a preset structured light encoded sequence onto the surface of the design to be scanned. To address the issue that a single-frequency stripe cannot simultaneously achieve both measurement accuracy and range, the projection unit employs a three-frequency heterodyne strategy, projecting a sequence with three different frequencies. , , A sequence of sinusoidal fringes.

[0082] The camera unit synchronously acquires stripe images modulated by the surface deformation of the design draft. For a frequency of... The Phase shift, light intensity distribution captured by the camera Expressed as:

[0083] ;

[0084] in Indicates background light intensity. Indicates the stripe tone system, This indicates the truncated phase information at the corresponding frequency. Indicates the first The phase shift amount per step. Background light is eliminated through a four-step or more phase shift algorithm. With reflectivity Interference, calculate the truncated phase .

[0085] The cutoff phase is calculated using the arctangent function. Restricted to arrive The phases exhibit a periodic, discontinuous distribution, making them unsuitable for direct depth calculations. The module employs a multi-frequency heterodyne method for phase unwrapping. Utilizing frequency... and The superposition of the truncated phases produces a beat frequency phase with an equivalent wavelength longer. When the beat frequency wavelength covers the entire field of view, the beat frequency phase is the unique absolute phase. Absolute phase With truncated phase The relationship satisfies: ;in The order of the stripe is an integer. The stripe order is determined step-by-step through pairwise heterodyne operations on the three frequencies. This restores discontinuous truncated phases to a monotonically continuous absolute phase distribution. This technique solves the phase ambiguity problem caused by step or discontinuous regions on the surface of the design draft, ensuring the uniqueness of the phase value.

[0086] After obtaining the absolute phase map, the module performs stereo matching using the epipolar constraints of the binocular cameras. Since the left and right cameras are rigorously calibrated, a point on the left image will necessarily have a corresponding point on the right image located on the corresponding epipolar line. Combining the uniqueness of the absolute phase value, pixels with the same phase value are searched along the epipolar line as corresponding points, and the disparity between these corresponding points in the left and right images is calculated. Based on the principle of triangulation, parallax is mapped to three-dimensional coordinates in physical space. Let the focal length of the binocular camera be... The baseline distance is Parallax is ,in and Let x and y be the horizontal coordinates of the left and right images, respectively, then the spatial depth coordinates of the pixels on the surface of the design draft are... calculate: Further derivation of the horizontal coordinates and vertical coordinates : ;in , These are the coordinates of the image plane.

[0087] After the above processing, the multimodal sensing module output includes A set of discrete points This refers to physical point cloud data. This technical solution combines the high precision of the phase-shifting method with the large-range deblurring capability of the multi-frequency heterodyne method to achieve high-density reconstruction of design draft surfaces with simple textures or drastic reflectivity variations. Epipolar constraints are used to narrow the matching search range and reduce the false matching rate. The final output physical point cloud data provides an accurate scale benchmark and topological foundation for subsequent discrete geometric modeling.

[0088] The discrete geometry modeling module uses Deloni triangulation to construct a simple complex mesh from physical point cloud data, calculates the Euclidean distance of the mesh edge length as the discrete Riemann metric, and constructs the discrete Hodge star operator.

[0089] Furthermore, discrete geometric modeling includes:

[0090] Traverse every common edge in the simple complex mesh;

[0091] Identify the two adjacent triangular faces shared by the common edge;

[0092] Determine the angles of the vertices opposite the common edge in these two triangular facets;

[0093] Calculate the cotangent of the angle between these two relative vertices;

[0094] Sum the two cotangent values ​​and take the average value. Assign the result to the weight coefficient of the common edge in the diagonal matrix of the discrete Hodge star operator.

[0095] Specifically, the module first reads in unordered 3D point cloud data, uses the projective Deloni triangulation algorithm to establish the topological connections between points, and generates a simple complex mesh composed of a series of triangular facets. Each vertex in the mesh corresponds to a 3D coordinate point in the point cloud. Based on this, the module calculates the coordinates of each edge in the mesh. The length of the connected vertices. and The length of the side. Calculate the Euclidean distance between the coordinates of the two vertices:

[0096] ;

[0097] This length Defined as the discrete Riemannian metric of a manifold surface, it quantifies the degree of stretching of the surface in a local region and serves as the physical benchmark for subsequently determining the accuracy of isometric mapping.

[0098] To perform differential form operations on a discrete mesh, the module constructs a discrete Hodge star operator. This operator establishes a mapping between the forms on the original mesh and the forms on the dual mesh. The specific computation is achieved by traversing all common edges within the mesh. For any common edge... The module retrieves the topological structure to identify two adjacent triangular faces that share the same edge, denoted as... and In a triangle In the middle, identification and edge The opposite vertex angle is ; in triangle In the middle, identification and edge The opposite vertex angle is The module calculates the cotangent values ​​of the two relative angles separately, sums them, and takes the average as the weight coefficient of that side in the Discrete Hodge Star operator. Calculation formula: ;in Represents the edge corresponding to the discrete Hodge star matrix. diagonal elements, The angle values ​​between the opposite vertices in the first adjacent triangle. This represents the angle value between the opposite vertices in the second adjacent triangle. For an edge located on the grid boundary, there is only one adjacent triangle, and in this case, the formula contains only one corresponding cotangent term.

[0099] After the above processing, the module outputs a simple complex mesh containing geometric and topological information, a set of discrete Riemannian metrics describing the physical properties of the side lengths, and a discrete Hodge star matrix describing the local geometric weights. The Hodge star operator, constructed using the cotangent formula, is mathematically equivalent to defining the stiffness matrix coefficients of the discrete Laplace-Beltrami operator. This processing transforms the geometric angle information of the design surface into weights in algebraic operations, enabling subsequent modules to directly solve partial differential equations such as the Poisson equation on the irregular triangular mesh. This accurately captures the curvature characteristics of the surface and calculates conformal mapping coordinates without resampling the mesh into a regular lattice, preserving the geometric accuracy of the original physical sampling.

[0100] The topology orientation correction module calculates the Gaussian curvature of the grid vertices based on discrete Riemannian metric values ​​and uses the Levi-Civita connection to solve the energy minimization equation to obtain the parallel moving field distributed along the geodesics.

[0101] Furthermore, topology orientation correction includes:

[0102] The difference between the sum of the vertex angles of all triangles surrounding a vertex inside the grid and the inscribed angle is used as the angular deficit to determine the discrete Gaussian curvature.

[0103] Construct a least-squares energy equation that includes a smoothing term and an integrity constraint term. The smoothing term is used to constrain the smooth transition of rotation angles between adjacent edges, and the integrity constraint term requires that the sum of rotation angles along a closed path equals the total curvature of the region enclosed by the path.

[0104] By solving the sparse linear equation system to minimize the energy equation, the rotation angle value of each edge in the grid is obtained.

[0105] Specifically, the module first determines the intrinsic geometric features of the mesh surface. For any internal vertex in the mesh... The module retrieves the set of all triangle faces that share a common vertex. It then uses the law of cosines and the input discrete Riemannian metric to calculate the facets of each triangle at the vertex. The vertex angle at that point. Calculate the vertex angle. The angular deficiency at the point is used as the discrete Gaussian curvature Calculation formula: ;in Represents vertices Discrete Gaussian curvature, For the vertex The number of connected triangles For the first Adjacent triangles at the vertex The interior angle at that point. This value directly reflects the degree of local curvature of the surface at that point. A non-zero value indicates that the region cannot be directly unfolded into a plane without distortion.

[0106] To establish a smooth vector field on a curved surface to guide texture unfolding, the module utilizes the Levi-Civita connection to construct a least-squares energy equation. This equation aims to find a set of rotation angles defined on the mesh edges such that the vector field propagating along these angles is as smooth as possible while satisfying curvature constraints. Energy Equation It includes smoothing terms and integrity constraints, expressed as follows:

[0107] ;

[0108] in For total energy, The edge to be solved The rotation angle adjustment value on The initial parallel translation component is determined by the geometry. Let be the set of all edges. These are Lagrange multipliers or weighting coefficients. For the set of all facets, Represents a piece of dough edge path, This represents the total curvature within the patch region. Smoothing term. The constraint minimizes the change in rotation angle between adjacent edges to ensure the continuity of vector field transformation; integrity constraint term. The sum of the rotation angles along any closed path must be exactly equal to the Gaussian curvature of the region enclosed by that path, in order to satisfy the topological requirement of the Gauss-Bonnet theorem.

[0109] The module transforms the energy minimization problem into a problem of solving a sparse linear equation system. Since the number of mesh edges is linearly related to the number of faces, the coefficient matrix exhibits a sparse, banded distribution. The linear equation system is solved using the Cholsky decomposition or the conjugate gradient method to obtain the optimal rotation angle value for each edge. By assigning this optimal rotation angle value to the edges of the mesh, a discrete parallel movement field is defined. This field specifies the rotation rule for tangent vectors when crossing mesh edges, ensuring that the covariant derivative remains zero when any tangent vector moves along this rule.

[0110] The module output includes a parallel translation field defined by the optimal rotation angle. This technical solution accurately quantifies the intrinsic curvature of discrete surfaces using angular deficit and overcomes the shortcomings of traditional path-dependent methods that generate cumulative errors on undulating surfaces by introducing an energy minimization method with integrity constraints. The obtained parallel translation field provides a globally consistent directional reference for subsequent conformal parameterization, ensuring that the unfolded 2D coordinate system does not flip or tear in its topology, thus maintaining the latitude and longitude logic of the design texture.

[0111] The conformal parameterized expansion module constructs an initial gradient field based on a parallel moving field, decomposes the initial gradient field using Hodge decomposition and forcibly removes the curl component, reconstructs and corrects the gradient field using the retained components, and solves the Poisson equation to obtain the two-dimensional expanded coordinates.

[0112] Furthermore, conformal parametric expansion includes:

[0113] Define the discrete forms of the gradient operator and curl operator;

[0114] The initial gradient field is projected onto a first subspace consisting of an irrotational field, a second subspace consisting of a divergence-free field, and a third subspace consisting of a harmonic field.

[0115] Extract the gradient component projection from the first subspace and the harmonic component projection from the third subspace;

[0116] Ignore the projection of the curl component in the second subspace;

[0117] The extracted gradient component projections and harmonic component projections are vector synthesized to generate a corrected gradient field that contains only conformal transformation features.

[0118] Conformal parametric expansion also includes:

[0119] Calculate the divergence value of the corrected gradient field at each grid vertex;

[0120] Construct a sparse coefficient matrix, which is composed of discrete Laplace-Beltrami operators, and the operators are weighted using the weights of discrete Hodge star operators;

[0121] Use the divergence value as the source term vector;

[0122] Introduce Dirichlet boundary conditions or Neumann boundary conditions to fix the degrees of freedom of the solution;

[0123] The sparse linear equations are solved using the conjugate gradient method to obtain the UV texture coordinates of each vertex on the two-dimensional plane.

[0124] The bicubic interpolation algorithm is used to map pixel grayscale values ​​from the original texture image based on UV texture coordinates.

[0125] Specifically, the module first defines the gradient operator and curl operator on the discrete grid. An initial gradient field is then constructed based on the input parallel translation field. Although the vector field maintains directional consistency locally, it still contains non-conformal shear components due to the non-flatness of the surface. According to the Hodge decomposition theorem, any tangent vector field can be orthogonally decomposed into a superposition of three subspaces: a first subspace composed of irrotational fields, a second subspace composed of divergence-free fields, and a third subspace composed of harmonic fields. Initial gradient field The decomposition formula is expressed as follows: ;in For the initial gradient field, The gradient component projection in the first subspace represents the pure scaling deformation; The projection of the curl component in the second subspace represents shear and rotational deformation. This represents the harmonic component projection in the third subspace, characterizing the overall topological properties of the system. The module performs filtering operations during computation to extract the gradient component projection from the first subspace. Projection of harmonic components with the third subspace At the same time, the curl component projection of the second subspace is forcibly ignored. The extracted gradient components are vector-synthesized with the harmonic components to generate the corrected gradient field. : This step removes shearing terms that cause texture distortion at the algebraic level, ensuring that the reconstructed vector field contains only the geometric features required for conformal transformation.

[0126] To transform the modified gradient field into specific planar coordinates, the module solves the Poisson equation. First, the modified gradient field is calculated. At each vertex of the grid divergence value at And define this set of divergence values ​​as the source term vector of the linear equation system. Construct a sparse coefficient matrix. This matrix is ​​composed of discrete Laplace-Beltrami operators, and its element values ​​are calculated using weighted averages of discrete Hodge star operators input from the discrete geometry modeling module. For mesh vertices... and Matrix elements Defined as:

[0127] ;

[0128] in and For the edge The diagonal angle. Construct a system of linear equations. ,in Let be the coordinate vector of the two-dimensional texture to be solved. Since the Laplacian matrix of a pure von Neumann boundary condition is singular, the module introduces Dirichlet or von Neumann boundary conditions to fix the degrees of freedom of the solution. Typically, the coordinate values ​​are fixed at the mesh center or corners to eliminate uncertainties in translation and rotation. The conjugate gradient method is used to iteratively solve this large sparse linear system of equations. Compared to direct inversion, this method significantly reduces memory consumption and improves computational speed. The obtained solution... That is, the UV texture coordinates of the mesh vertices on the two-dimensional Euclidean plane. .

[0129] After obtaining the UV texture coordinates, the module performs pixel mapping from the 3D surface to the 2D image. Since the calculated UV coordinates are usually located at non-integer positions, the module employs a bicubic interpolation algorithm. For each pixel in the target image, the module finds the corresponding neighboring pixels in the original texture image based on its UV coordinates, fits the grayscale variation surface using a cubic polynomial, and calculates the grayscale or color value of that point. Finally, the module outputs the 2D unfolded coordinates, which remove shear distortion and preserve local angles, along with the corresponding preliminary correction image. This image serves as the geometric reference for the subsequent active optical verification module to generate the inverse projection pattern.

[0130] The active optical verification module uses two-dimensional unfolded coordinates to establish an inverse mapping relationship, converts the standard grid into an inverse projection image and projects it back onto the physical surface, and calculates the difference norm between the acquired feedback image and the standard phase to generate a phase residual field.

[0131] Furthermore, active optical verification includes:

[0132] In a two-dimensional unfolded coordinate system, determine the two-dimensional grid patch to which each pixel in the inverse projected image belongs;

[0133] Calculate the centroid coordinates of the pixel in the 2D mesh area;

[0134] By interpolating the vertex coordinates of the corresponding facet of the 3D simple complex mesh using the centroid coordinates, the 3D physical space coordinates of the pixel are obtained.

[0135] By using the intrinsic and extrinsic parameter matrices of the projection unit, the three-dimensional physical space coordinates are transformed into pixel row and column coordinates of the projection plane, generating the inverse projection image to be projected.

[0136] Active optical verification also includes:

[0137] The measured phase distribution of the physical surface is obtained by phase-shift demodulating the acquired feedback image;

[0138] The corresponding theoretical phase distribution is directly generated based on the generation logic of the inverse projection image;

[0139] Pixel-by-pixel alignment is performed between the measured phase distribution and the theoretical phase distribution;

[0140] Calculate the L2 norm of the difference between the measured phase value and the theoretical phase value at the same pixel location, and use this norm as the phase residual value at that location.

[0141] Specifically, the module first establishes an inverse mapping link from the two-dimensional parametric plane to the projector imaging plane. A standard grid image is set as the reference, defined in a two-dimensional unfolded coordinate system. In order to accurately project the reference image back onto the physical design surface, it is necessary to calculate the light intensity distribution that the projector should project.

[0142] The module iterates through each pixel in the standard grid image. The process involves retrieving the corresponding 2D mesh patch within a simple complex mesh constructed from the unfolded 2D coordinate system. Once the patch is determined, the pixel's position is calculated. The barycentric coordinates in this two-dimensional patch The centroid coordinates satisfy... ,and ,in Let be the coordinates of the three vertices of the two-dimensional patch.

[0143] Using the above barycentric coordinates, the vertex coordinates of the corresponding facets in the 3D simplex mesh are obtained. Perform linear interpolation to obtain the three-dimensional physical space coordinates of the pixel. : After obtaining the three-dimensional physical coordinates, the projection element intrinsic parameter matrix obtained during the system calibration phase is used. With extrinsic matrix Transform the three-dimensional coordinates into pixel row and column coordinates of the projector image plane. The transformation model is as follows:

[0144] ;

[0145] in As a scale factor, For the projector's focal length, Principal point coordinates Let be a rotation matrix. This is the translation vector. This transformation generates the inversely projected image after distortion pre-compensation.

[0146] The projection unit projects the generated inverse projection image, while the camera unit simultaneously acquires the feedback image presented on the physical surface. The module performs phase-shift demodulation on the feedback image to obtain the measured phase distribution actually presented on the physical surface. .

[0147] Simultaneously, based on the generation logic of the inverse projection image and the geometric definition of the standard mesh, the corresponding theoretical phase distribution is directly generated. The theoretical phase distribution represents the phase value that a physical surface should exhibit under the assumption of ideal isometric mapping.

[0148] The module performs pixel-by-pixel alignment between the measured phase distribution and the theoretical phase distribution. At the same pixel location... At that location, calculate the L2 norm of the difference between the two values, and define the result as the phase residual value at that location. :

[0149] in This represents the Euclidean norm. The generated phase residual field intuitively reflects the deviation between the unfolded coordinates calculated by the current mathematical model and the actual shape of the physical entity. Non-zero residual values ​​indicate the presence of physical wrinkles or metric distortions in the region that have not yet been captured by the mathematical model. This residual field data is then used as input to the closed-loop feedback compensation module, driving the system to iteratively correct the discrete Riemann metric.

[0150] The closed-loop feedback compensation module calculates the gradient flow of the phase residual field, updates the discrete Riemann metric value based on the gradient flow using the Lie derivative, and returns to the discrete geometric modeling module to perform iterations until the phase residual field satisfies the convergence condition.

[0151] Furthermore, closed-loop feedback compensation includes:

[0152] Calculate the spatial gradient vector of the phase residual field on the surface of the discrete manifold;

[0153] The spatial gradient vector is defined as the deformation velocity field of the manifold;

[0154] Calculate the Lie derivative of the current discrete Riemannian metric tensor along the deformation velocity field, that is, calculate the infinitesimal deformation rate of the metric tensor under the action of the velocity field.

[0155] The deformation rate is multiplied by the adaptive step size coefficient and then added to the current discrete metric value of the side length to obtain a new metric value containing physical deformation compensation information.

[0156] Specifically, the module reads the phase residual field defined on the surface of the discrete manifold. This scalar field reflects the potential energy difference between the current geometric unfolding state and the physical reality. Calculate the spatial gradient vector of this scalar field on the tangent space of the manifold. The negative direction of the spatial gradient vector is defined as the deformation velocity field of the manifold. This vector field indicates the tendency for grid nodes to move in order to reduce the system's potential energy. Deformation velocity field. The definition is as follows: ;in Represents the deformation velocity field vector. The inverse matrix components of the current metric tensor. Let be the partial derivative of the phase residual field with respect to the local coordinates. These are the basis vectors of the tangent space. This step establishes the mapping from the error distribution to the geometric adjustment direction.

[0157] To correct for the discrete metric of side length, the module computes the current discrete Riemannian metric tensor. Along the deformation velocity field Li Daoshu The Lie derivative describes the infinitesimal rate of change of a metric tensor as a vector flow drags along a streamline, i.e., the dynamic trend of the geometry evolving with the error flow. For each edge in the discrete mesh... Its corresponding metric is the rate of change of the tensor. Calculated by projecting the Lie derivative onto the edge direction:

[0158] ;

[0159] in For the edge The rate of change of length, For the border The unit tangent vector in the direction, This represents the Ligand operation. This calculation quantifies the physical tendency for each mesh edge to stretch or shrink under the current error.

[0160] After obtaining the deformation rate, the module uses the Euler integral method to numerically update the discrete metric values. An adaptive step size coefficient is defined. This coefficient decays with the number of iterations to ensure convergence stability. The deformation rate is multiplied by the step size coefficient and then accumulated into the current discrete metric value for the side length to generate a new metric value. :

[0161] ;

[0162] in This is the length of the edge before the update. This is the new side length, incorporating physical deformation compensation information. The module determines whether the global norm of the phase residual field is less than a preset convergence threshold. If the convergence condition is not met, the module will generate a new set of metrics. The feedback is sent to the discrete geometry modeling module. Based on this new metric, the discrete geometry modeling module reconstructs the discrete Hodge star operator and triggers subsequent topological orientation correction and conformal parameterization expansion steps, forming a closed-loop control. This technical solution, by introducing Lie derivative number flow, transforms the unstructured errors of physical space into metric tensor correction quantities under the Riemannian geometric framework, enabling the mathematical model to gradually approximate the true physical tensile properties of paper material, thus solving the problem that pure geometric mapping methods cannot handle non-uniform physical deformation.

[0163] Example 2:

[0164] In the digital archiving of large-format precision engineering drawings in fields such as aerospace, shipbuilding, and historical building restoration, the original documents often exhibit complex non-rigid composite deformations due to long-term curling, moisture, or material aging. These valuable documents typically require non-contact, high-fidelity capture to avoid physical damage. However, existing structured scanning and correction technologies have significant shortcomings when handling such objects: on the one hand, traditional algorithms often rely on the assumption of uniform material elasticity for simple visual flattening, ignoring the shear distortion caused by the anisotropy of paper fibers, resulting in topological logic errors in the corrected engineering lines; on the other hand, existing manifold unfolding techniques are mostly "open-loop" calculations, lacking closed-loop accuracy verification methods for physical entities, and failing to address the metric tensor distortion problem during surface parameterization. This leads to scale inconsistencies between the center and edge areas in the digitized drawings, failing to meet the stringent requirements for geometric dimension restoration in subsequent CAD reverse modeling or precision engineering measurements. To address these issues, this invention provides a correction method for rapid capture of design drafts, the structure of which is as follows: Figure 4 As shown. The specific implementation process of this method is as follows:

[0165] The multimodal sensing module performs photoelectric conversion. The projection unit projects sinusoidal fringes of different frequencies in a time sequence, while the binocular camera synchronously captures two-dimensional images modulated by the geometric deformation of the design surface. Utilizing the multi-frequency heterodyne principle, the truncated phases of different frequencies are superimposed to eliminate the periodic ambiguity of single-frequency phases, thus calculating a unique absolute phase distribution across the entire field of view. Combining the triangulation principle of binocular stereo vision, a mapping relationship between image pixel coordinates and physical space coordinates is established, outputting high-precision three-dimensional point cloud data. This step uses optical encoding to transform the physical form of the design into a discrete set of points that can be processed by a computer, overcoming the deficiency of traditional image processing in lacking depth information.

[0166] The discrete geometry modeling module transforms discrete point clouds into mathematical models with topological connections. The Deloni triangulation algorithm is applied to connect the point clouds to generate simple complex meshes, ensuring that the mesh surface quality meets the requirements of finite element analysis. The Euclidean length of each connecting edge in the mesh is calculated and defined as a discrete Riemannian metric, which quantifies the local physical stretching properties of the surface. Based on the mesh geometry, the geometric ratio between dual edges and primal edges is calculated, constructing a discrete Hodge star operator. This operator transforms geometric information into weighting coefficients in algebraic operations, providing a computational basis for subsequent differential operations on irregular meshes.

[0167] The topology orientation correction module addresses the orientation consistency issue during surface unfolding. It calculates the angular deficit at mesh vertices based on discrete Riemannian metric values, determines the discrete Gaussian curvature at each point, and identifies the intrinsic curvature characteristics of the surface. Based on Levi-Civita connection theory, an energy function incorporating smoothing terms and integrity constraints is established, and solving this function yields the optimal rotation angle at the mesh edges. This rotation angle defines a parallel movement field distributed along geodesics, ensuring that the covariant derivative of the tangent vector remains zero during transmission across the mesh surface. This step locks in the latitude and longitude logic of texture unfolding at the topological level, preventing texture curl distortion caused by curvature changes.

[0168] The conformal parametric expansion module performs the core distortion correction operation. An initial gradient field is constructed based on the parallel movement field. Using the Hodge decomposition theorem, this incompatible vector field is orthogonally decomposed into irrotational gradient components, divergence-free curl components, and harmonic components. Since the curl component corresponds to non-conformal shear deformation, it is forcibly removed during reconstruction, retaining only the gradient and harmonic components to generate the corrected gradient field. Using the divergence of the corrected gradient field as the source term, the Poisson equation is constructed and solved using the discrete Hodge star operator, obtaining the parametric coordinates of the mesh vertices in the two-dimensional plane. This process mathematically eliminates shear distortion, achieving conformal mapping.

[0169] An active optical verification module establishes a physical verification mechanism. Using calculated two-dimensional unfolded coordinates, an inverse mapping index from the plane to the curved manifold is established, transforming the standard orthogonal mesh pattern into a reverse-projected image adapted to the current surface morphology. The projection unit controls the projection of this image back onto the physical design surface, and the camera acquires the feedback image. The feedback image undergoes phase demodulation and is compared with the theoretical phase of the standard mesh to generate a phase residual field. This residual field directly reflects the measurement deviation between the current mathematical model and the physical entity, and can detect microscopic physical errors such as non-uniform stretching of the paper material.

[0170] The closed-loop feedback compensation module utilizes physical error correction to refine the mathematical model. The phase residual field is considered as the potential energy driving manifold deformation, and its gradient flow on the manifold surface is calculated. The rate of change of the current discrete Riemann metric tensor along this gradient flow is calculated using the Lie derivative, quantifying the trend of the metric tensor's evolution with the error flow. Based on this rate of change, the initial discrete Riemann metric value in step S2 is iteratively corrected, and the corrected metric value is used to re-trigger the calculation process in steps S3 to S5. The system repeats the above process until the phase residual field converges to a preset threshold, thereby outputting a structured design draft that has undergone dual physical and mathematical calibration, solving the problem that a single mathematical model cannot adapt to the complex physical material properties.

[0171] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A structured scanning platform for rapid capture of design drafts, characterized in that, Includes the following modules: The multimodal sensing module projects a phase-shifted fringe sequence and acquires modulated images, uses the multi-frequency heterodyne method to solve the absolute phase, and obtains physical point cloud data of the design surface based on triangulation. The discrete geometry modeling module uses Deloni triangulation to construct a simple complex mesh from physical point cloud data, calculates the Euclidean distance of the mesh edge length as the discrete Riemann metric, and constructs the discrete Hodge star operator. The topology orientation correction module calculates the Gaussian curvature of the grid vertices based on discrete Riemannian metric values ​​and uses the Levi-Civita connection to solve the energy minimization equation to obtain the parallel moving field distributed along the geodesics. The conformal parameterized expansion module constructs an initial gradient field based on a parallel moving field, decomposes the initial gradient field using Hodge decomposition and forcibly removes the curl component, reconstructs and corrects the gradient field using the retained components, and solves the Poisson equation to obtain the two-dimensional expanded coordinates. The active optical verification module uses two-dimensional unfolded coordinates to establish an inverse mapping relationship, converts the standard grid into an inverse projection image and projects it back onto the physical surface, and calculates the difference norm between the acquired feedback image and the standard phase to generate a phase residual field. The closed-loop feedback compensation module calculates the gradient flow of the phase residual field, updates the discrete Riemann metric value based on the gradient flow using the Lie derivative, and returns to the discrete geometric modeling module to perform iterations until the phase residual field satisfies the convergence condition.

2. The structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The multimodal sensing includes: Project a sequence of sinusoidal fringes with three different frequencies onto the design draft; The acquired modulated image is subjected to phase unwrapping operation to restore the truncated phase to continuous phase; Phase ambiguity is eliminated by utilizing the principle of phase difference between different frequencies, thus obtaining a unique absolute phase distribution; Stereo matching of left and right images is performed based on epipolar constraints of a binocular camera, and the three-dimensional depth coordinates of each pixel are calculated using the parallax principle.

3. The structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The discrete geometric modeling includes: Traverse every common edge in the simple complex mesh; Identify the two adjacent triangular faces shared by the common edge; Determine the angles of the vertices opposite the common edge in these two triangular facets; Calculate the cotangent of the angle between these two relative vertices; Sum the two cotangent values ​​and take the average value. Assign the result to the weight coefficient of the common edge in the diagonal matrix of the discrete Hodge star operator.

4. The structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The topology orientation correction includes: The difference between the sum of the vertex angles of all triangles surrounding a vertex inside the grid and the inscribed angle is used as the angular deficit to determine the discrete Gaussian curvature. Construct a least-squares energy equation that includes a smoothing term and an integrity constraint term. The smoothing term is used to constrain the smooth transition of rotation angles between adjacent edges, and the integrity constraint term requires that the sum of rotation angles along a closed path equals the total curvature of the region enclosed by the path. The rotation angle of each edge in the grid is obtained by minimizing the energy equation by solving the sparse linear equation system.

5. A structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The conformal parametric expansion includes: Define the discrete forms of the gradient operator and curl operator; The initial gradient field is projected onto a first subspace consisting of an irrotational field, a second subspace consisting of a divergence-free field, and a third subspace consisting of a harmonic field. Extract the gradient component projection from the first subspace and the harmonic component projection from the third subspace; Ignore the projection of the curl component in the second subspace; The extracted gradient component projections and harmonic component projections are vector synthesized to generate a corrected gradient field that contains only conformal transformation features.

6. A structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The conformal parametric expansion also includes: Calculate the divergence value of the modified gradient field at each grid vertex; Construct a sparse coefficient matrix, which is composed of discrete Laplace-Beltrami operators, and the operators are weighted using the weights of discrete Hodge star operators; Use the divergence value as the source term vector; Introduce Dirichlet boundary conditions or Neumann boundary conditions to fix the degrees of freedom of the solution; The sparse linear equations are solved using the conjugate gradient method to obtain the UV texture coordinates of each vertex on the two-dimensional plane. The bicubic interpolation algorithm is used to map pixel grayscale values ​​from the original texture image based on UV texture coordinates.

7. A structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The active optical verification includes: In a two-dimensional unfolded coordinate system, determine the two-dimensional grid patch to which each pixel in the inverse projected image belongs; Calculate the centroid coordinates of the pixel within the two-dimensional grid patch; The vertex coordinates of the corresponding facet of the three-dimensional simple complex mesh are interpolated using the centroid coordinates to obtain the three-dimensional physical space coordinates of the pixel. Using the intrinsic and extrinsic parameter matrices of the projection unit, the three-dimensional physical space coordinates are transformed into pixel row and column coordinates of the projection plane to generate the inverse projection image to be projected.

8. A structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The active optical verification also includes: The measured phase distribution of the physical surface is obtained by phase-shift demodulating the acquired feedback image; The corresponding theoretical phase distribution is directly generated based on the generation logic of the inverse projection image; Pixel-by-pixel alignment is performed between the measured phase distribution and the theoretical phase distribution; Calculate the L2 norm of the difference between the measured phase value and the theoretical phase value at the same pixel location, and use this norm as the phase residual value at that location.

9. A structured scanning platform for rapid capture of design drafts according to claim 1, characterized in that, The closed-loop feedback compensation includes: Calculate the spatial gradient vector of the phase residual field on the surface of the discrete manifold; The spatial gradient vector is defined as the deformation velocity field of the manifold; Calculate the Lie derivative of the current discrete Riemannian metric tensor along the deformation velocity field, that is, calculate the infinitesimal deformation rate of the metric tensor under the action of the velocity field. The deformation rate is multiplied by the adaptive step size coefficient and then added to the current discrete metric value of the side length to obtain a new metric value containing physical deformation compensation information.

10. A method for rapid capture and correction of design drafts, characterized in that, A structured scanning platform for rapid capture of design drafts as described in any one of claims 1-9 includes the following steps: S1. By projecting phase-shifted fringe sequences and acquiring modulated images, the absolute phase is calculated using the multi-frequency heterodyne method, and physical point cloud data of the design surface is obtained based on triangulation. S2. Using Deloni triangulation, the physical point cloud data is constructed into a simple complex mesh. The Euclidean distance of the mesh edge length is calculated as the discrete Riemann metric, and the discrete Hodge star operator is constructed. S3. Calculate the Gaussian curvature of the grid vertices based on the discrete Riemannian metric, and use the Levi-Civita connection to solve the minimum energy equation to obtain the parallel moving field distributed along the geodesic. S4. Construct an initial gradient field based on the parallel moving field, decompose the initial gradient field using Hodge decomposition and forcibly remove the curl component, reconstruct the corrected gradient field using the retained components and solve the Poisson equation to obtain the two-dimensional expanded coordinates. S5. Establish an inverse mapping relationship using two-dimensional unfolded coordinates, convert the standard grid into an inverse projection image and project it back onto the physical surface, and calculate the difference norm between the acquired feedback image and the standard phase to generate the phase residual field. S6. Calculate the gradient flow of the phase residual field, update the discrete Riemann metric value based on the gradient flow using the Lie derivative, and return to the discrete geometry modeling module to perform iterations until the phase residual field satisfies the convergence condition.

Images